imo.imo1981_q3
⟷
Archive.Imo.Imo1981Q3
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
-import Data.Nat.Fib
+import Data.Nat.Fib.Basic
import Mathbin.Tactic.Linarith.Default
#align_import imo.imo1981_q3 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -174,7 +174,7 @@ theorem m_n_bounds {m n : ℕ} (h1 : NatPredicate N m n) : m ≤ fib K ∧ n ≤
_ ≤ fib (K + 1) := fib_mono h6
· have h7 : N < n := by
have h8 : K + 2 ≤ k + 1 := succ_le_succ (not_lt.mp h2)
- rw [← fib_add_two] at HK
+ rw [← fib_add_two] at HK
calc
N < fib (K + 2) := HK
_ ≤ fib (k + 1) := (fib_mono h8)
@@ -192,7 +192,7 @@ theorem k_bound {m n : ℤ} (h1 : ProblemPredicate N m n) : m ^ 2 + n ^ 2 ≤ M
by
have h2 : 0 ≤ m := h1.m_range.left.le
have h3 : 0 ≤ n := h1.n_range.left.le
- rw [← nat_abs_of_nonneg h2, ← nat_abs_of_nonneg h3] at h1 ; clear h2 h3
+ rw [← nat_abs_of_nonneg h2, ← nat_abs_of_nonneg h3] at h1; clear h2 h3
obtain ⟨h4 : m.nat_abs ≤ fib K, h5 : n.nat_abs ≤ fib (K + 1)⟩ := m_n_bounds HK h1
have h6 : m ^ 2 ≤ fib K ^ 2 := nat_abs_le_iff_sq_le.mp h4
have h7 : n ^ 2 ≤ fib (K + 1) ^ 2 := nat_abs_le_iff_sq_le.mp h5
@@ -219,7 +219,7 @@ numbers in this range, and thus provide the maximum of `specified_set`.
theorem imo1981_q3 : IsGreatest (specifiedSet 1981) 3524578 :=
by
have := fun h => @solution_greatest 1981 16 h 3524578
- simp only [show fib (16 : ℕ) = 987 ∧ fib (16 + 1 : ℕ) = 1597 by norm_num [fib_add_two]] at this
+ simp only [show fib (16 : ℕ) = 987 ∧ fib (16 + 1 : ℕ) = 1597 by norm_num [fib_add_two]] at this
apply_mod_cast this <;> norm_num [problem_predicate_iff]
#align imo1981_q3 imo1981_q3
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
-import Mathbin.Data.Nat.Fib
+import Data.Nat.Fib
import Mathbin.Tactic.Linarith.Default
#align_import imo.imo1981_q3 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-
-! This file was ported from Lean 3 source module imo.imo1981_q3
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Nat.Fib
import Mathbin.Tactic.Linarith.Default
+#align_import imo.imo1981_q3 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
/-!
# IMO 1981 Q3
mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
! This file was ported from Lean 3 source module imo.imo1981_q3
-! leanprover-community/mathlib commit 2d6f88c296da8df484d7f5b9ee1d10910ab473a2
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Tactic.Linarith.Default
/-!
# IMO 1981 Q3
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Determine the maximum value of `m ^ 2 + n ^ 2`, where `m` and `n` are integers in
`{1, 2, ..., 1981}` and `(n ^ 2 - m * n - m ^ 2) ^ 2 = 1`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -158,8 +158,6 @@ satisfying `nat_predicate m n N` are `fib K` and `fib (K+1)`, respectively.
-/
variable {K : ℕ} (HK : N < fib K + fib (K + 1)) {N}
-include HK
-
theorem m_n_bounds {m n : ℕ} (h1 : NatPredicate N m n) : m ≤ fib K ∧ n ≤ fib (K + 1) :=
by
obtain ⟨k : ℕ, hm : m = fib k, hn : n = fib (k + 1)⟩ := h1.imp_fib m
@@ -190,8 +188,6 @@ We spell out the consequences of this result for `specified_set N` here.
-/
variable {M : ℕ} (HM : M = fib K ^ 2 + fib (K + 1) ^ 2)
-include HM
-
theorem k_bound {m n : ℤ} (h1 : ProblemPredicate N m n) : m ^ 2 + n ^ 2 ≤ M :=
by
have h2 : 0 ≤ m := h1.m_range.left.le
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -61,7 +61,6 @@ theorem m_le_n {m n : ℤ} (h1 : ProblemPredicate N m n) : m ≤ n :=
calc
1 = (n ^ 2 - m * n - m ^ 2) ^ 2 := h1.eq_one.symm
_ = (n * (n - m) - m ^ 2) ^ 2 := by ring
-
have h4 : n * (n - m) - m ^ 2 < -1 := by nlinarith [h1.n_range.left]
have h5 : 1 < (n * (n - m) - m ^ 2) ^ 2 := by nlinarith
exact h5.ne h3
@@ -72,7 +71,6 @@ theorem eq_imp_1 {n : ℤ} (h1 : ProblemPredicate N n n) : n = 1 :=
calc
_ = (n ^ 2 - n * n - n ^ 2) ^ 2 := by simp [sq, mul_assoc]
_ = 1 := h1.eq_one
-
eq_one_of_mul_eq_one_right h1.m_range.left.le this
#align imo1981_q3.problem_predicate.eq_imp_1 Imo1981Q3.ProblemPredicate.eq_imp_1
@@ -89,14 +87,12 @@ theorem reduction {m n : ℤ} (h1 : ProblemPredicate N m n) (h2 : 1 < n) :
calc
_ < n := sub_lt_self n h1.m_range.left
_ ≤ N := h1.n_range.right
-
exact ⟨h5, h6.le⟩
-- eq_one:
·
calc
_ = (n ^ 2 - m * n - m ^ 2) ^ 2 := by ring
_ = 1 := h1.eq_one
-
#align imo1981_q3.problem_predicate.reduction Imo1981Q3.ProblemPredicate.reduction
end ProblemPredicate
@@ -174,12 +170,10 @@ theorem m_n_bounds {m n : ℕ} (h1 : NatPredicate N m n) : m ≤ fib K ∧ n ≤
calc
m = fib k := hm
_ ≤ fib K := fib_mono h3
-
· have h6 : k + 1 ≤ K + 1 := succ_le_succ h3
calc
n = fib (k + 1) := hn
_ ≤ fib (K + 1) := fib_mono h6
-
· have h7 : N < n := by
have h8 : K + 2 ≤ k + 1 := succ_le_succ (not_lt.mp h2)
rw [← fib_add_two] at HK
@@ -187,7 +181,6 @@ theorem m_n_bounds {m n : ℕ} (h1 : NatPredicate N m n) : m ≤ fib K ∧ n ≤
N < fib (K + 2) := HK
_ ≤ fib (k + 1) := (fib_mono h8)
_ = n := hn.symm
-
have h9 : n ≤ N := h1.n_le_N
exact absurd h7 h9.not_lt
#align imo1981_q3.m_n_bounds Imo1981Q3.m_n_bounds
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090
@@ -163,7 +163,7 @@ theorem m_n_bounds {m n : ℕ} (h1 : NatPredicate N m n) : m ≤ fib K ∧ n ≤
rw [← fib_add_two] at HK
calc
N < fib (K + 2) := HK
- _ ≤ fib (k + 1) := (fib_mono h8)
+ _ ≤ fib (k + 1) := fib_mono h8
_ = n := hn.symm
have h9 : n ≤ N := h1.n_le_N
exact absurd h7 h9.not_lt
@@ -149,7 +149,7 @@ variable {K : ℕ} (HK : N < fib K + fib (K + 1)) {N}
theorem m_n_bounds {m n : ℕ} (h1 : NatPredicate N m n) : m ≤ fib K ∧ n ≤ fib (K + 1) := by
obtain ⟨k : ℕ, hm : m = fib k, hn : n = fib (k + 1)⟩ := h1.imp_fib m
by_cases h2 : k < K + 1
- · have h3 : k ≤ K := lt_succ_iff.mp h2
+ · have h3 : k ≤ K := Nat.lt_succ_iff.mp h2
constructor
· calc
m = fib k := hm
@@ -207,5 +207,5 @@ theorem imo1981_q3 : IsGreatest (specifiedSet 1981) 3524578 := by
apply this
· decide
· decide
- · norm_num [ProblemPredicate_iff]; decide
+ · norm_num [problemPredicate_iff]; decide
#align imo1981_q3 imo1981_q3
Data.Nat.Fib
→ Data.Nat.Fib.Basic
(#8576)
This was postponed to after the Zeckendorf PR.
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib.Data.Int.Lemmas
-import Mathlib.Data.Nat.Fib
+import Mathlib.Data.Nat.Fib.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
exact_mod_cast
tactic with mod_cast
elaborator where possible (#8404)
We still have the exact_mod_cast
tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast
are the ones that don't work using the term elaborator by itself.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -97,25 +97,25 @@ namespace NatPredicate
variable {N}
-nonrec theorem m_le_n {m n : ℕ} (h1 : NatPredicate N m n) : m ≤ n := by exact_mod_cast h1.m_le_n
+nonrec theorem m_le_n {m n : ℕ} (h1 : NatPredicate N m n) : m ≤ n := mod_cast h1.m_le_n
#align imo1981_q3.nat_predicate.m_le_n Imo1981Q3.NatPredicate.m_le_n
-nonrec theorem eq_imp_1 {n : ℕ} (h1 : NatPredicate N n n) : n = 1 := by exact_mod_cast h1.eq_imp_1
+nonrec theorem eq_imp_1 {n : ℕ} (h1 : NatPredicate N n n) : n = 1 := mod_cast h1.eq_imp_1
#align imo1981_q3.nat_predicate.eq_imp_1 Imo1981Q3.NatPredicate.eq_imp_1
nonrec theorem reduction {m n : ℕ} (h1 : NatPredicate N m n) (h2 : 1 < n) :
NatPredicate N (n - m) m := by
have : m ≤ n := h1.m_le_n
- exact_mod_cast h1.reduction (by exact_mod_cast h2)
+ exact mod_cast h1.reduction (mod_cast h2)
#align imo1981_q3.nat_predicate.reduction Imo1981Q3.NatPredicate.reduction
-theorem n_pos {m n : ℕ} (h1 : NatPredicate N m n) : 0 < n := by exact_mod_cast h1.n_range.left
+theorem n_pos {m n : ℕ} (h1 : NatPredicate N m n) : 0 < n := mod_cast h1.n_range.left
#align imo1981_q3.nat_predicate.n_pos Imo1981Q3.NatPredicate.n_pos
-theorem m_pos {m n : ℕ} (h1 : NatPredicate N m n) : 0 < m := by exact_mod_cast h1.m_range.left
+theorem m_pos {m n : ℕ} (h1 : NatPredicate N m n) : 0 < m := mod_cast h1.m_range.left
#align imo1981_q3.nat_predicate.m_pos Imo1981Q3.NatPredicate.m_pos
-theorem n_le_N {m n : ℕ} (h1 : NatPredicate N m n) : n ≤ N := by exact_mod_cast h1.n_range.right
+theorem n_le_N {m n : ℕ} (h1 : NatPredicate N m n) : n ≤ N := mod_cast h1.n_range.right
set_option linter.uppercaseLean3 false in
#align imo1981_q3.nat_predicate.n_le_N Imo1981Q3.NatPredicate.n_le_N
This is the supremum of
along with some minor fixes from failures on nightly-testing as Mathlib master
is merged into it.
Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.
I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0
branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.
In particular this includes adjustments for the Lean PRs
We can get rid of all the
local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)
macros across Mathlib (and in any projects that want to write natural number powers of reals).
Changes the default behaviour of simp
to (config := {decide := false})
. This makes simp
(and consequentially norm_num
) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp
or norm_num
to decide
or rfl
, or adding (config := {decide := true})
.
This changed the behaviour of simp
so that simp [f]
will only unfold "fully applied" occurrences of f
. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true })
. We may in future add a syntax for this, e.g. simp [!f]
; please provide feedback! In the meantime, we have made the following changes:
(config := { unfoldPartialApp := true })
in some places, to recover the old behaviour@[eqns]
to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp
and Function.flip
.This change in Lean may require further changes down the line (e.g. adding the !f
syntax, and/or upstreaming the special treatment for Function.comp
and Function.flip
, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!
Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>
@@ -129,7 +129,7 @@ theorem imp_fib {n : ℕ} : ∀ m : ℕ, NatPredicate N m n → ∃ k : ℕ, m =
obtain (rfl : 1 = n) | (h4 : 1 < n) := (succ_le_iff.mpr h2.n_pos).eq_or_lt
· use 1
have h5 : 1 ≤ m := succ_le_iff.mpr h2.m_pos
- simpa [fib_one, fib_two] using (h3.antisymm h5 : m = 1)
+ simpa [fib_one, fib_two, (by decide : 1 + 1 = 2)] using (h3.antisymm h5 : m = 1)
· obtain (rfl : m = n) | (h6 : m < n) := h3.eq_or_lt
· exact absurd h2.eq_imp_1 (Nat.ne_of_gt h4)
· have h7 : NatPredicate N (n - m) m := h2.reduction h4
@@ -205,5 +205,7 @@ theorem imo1981_q3 : IsGreatest (specifiedSet 1981) 3524578 := by
have := fun h => @solution_greatest 1981 16 h 3524578
norm_num at this
apply this
- norm_num [ProblemPredicate_iff]
+ · decide
+ · decide
+ · norm_num [ProblemPredicate_iff]; decide
#align imo1981_q3 imo1981_q3
norm_num
was passing the wrong syntax node to elabSimpArgs
when elaborating, which essentially had the effect of ignoring all arguments it was passed, i.e. norm_num [add_comm]
would not try to commute addition in the simp step.
The fix itself is very simple (though not obvious to debug!), probably using TSyntax more would help avoid such issues in future.
Due to this bug many norm_num [blah]
became rw [blah]; norm_num
or similar, sometimes with porting notes, sometimes not, we fix these porting notes and other regressions during the port also.
Interestingly cancel_denoms
uses norm_num [<- mul_assoc]
internally, so cancel_denoms
also got stronger with this change.
@@ -203,8 +203,7 @@ numbers in this range, and thus provide the maximum of `specifiedSet`.
-/
theorem imo1981_q3 : IsGreatest (specifiedSet 1981) 3524578 := by
have := fun h => @solution_greatest 1981 16 h 3524578
- simp only [show fib (16 : ℕ) = 987 ∧ fib (16 + 1 : ℕ) = 1597 by norm_num [fib_add_two]] at this
- apply_mod_cast this trivial trivial
- rw [ProblemPredicate_iff]
- norm_num
+ norm_num at this
+ apply this
+ norm_num [ProblemPredicate_iff]
#align imo1981_q3 imo1981_q3
@@ -2,17 +2,14 @@
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-
-! This file was ported from Lean 3 source module imo.imo1981_q3
-! leanprover-community/mathlib commit 2d6f88c296da8df484d7f5b9ee1d10910ab473a2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Int.Lemmas
import Mathlib.Data.Nat.Fib
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
+#align_import imo.imo1981_q3 from "leanprover-community/mathlib"@"2d6f88c296da8df484d7f5b9ee1d10910ab473a2"
+
/-!
# IMO 1981 Q3
This is the second half of the changes originally in #5699, removing all occurrences of ;
after a space and implementing a linter rule to enforce it.
In most cases this 2-character substring has a space after it, so the following command was run first:
find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;
The remaining cases were few enough in number that they were done manually.
@@ -180,7 +180,7 @@ variable {M : ℕ} (HM : M = fib K ^ 2 + fib (K + 1) ^ 2)
theorem k_bound {m n : ℤ} (h1 : ProblemPredicate N m n) : m ^ 2 + n ^ 2 ≤ M := by
have h2 : 0 ≤ m := h1.m_range.left.le
have h3 : 0 ≤ n := h1.n_range.left.le
- rw [← natAbs_of_nonneg h2, ← natAbs_of_nonneg h3] at h1 ; clear h2 h3
+ rw [← natAbs_of_nonneg h2, ← natAbs_of_nonneg h3] at h1; clear h2 h3
obtain ⟨h4 : m.natAbs ≤ fib K, h5 : n.natAbs ≤ fib (K + 1)⟩ := m_n_bounds HK h1
have h6 : m ^ 2 ≤ (fib K : ℤ) ^ 2 := Int.natAbs_le_iff_sq_le.mp h4
have h7 : n ^ 2 ≤ (fib (K + 1) : ℤ) ^ 2 := Int.natAbs_le_iff_sq_le.mp h5
Replace some porting notes about refine_struct
with uses of refine'
. We only really miss refine_struct
in situations where we later used pi_instance_derive_field
.
I also exercised some editorial discretion to remove some porting notes about refine_struct
when the original usage was (in my opinion) obfuscatory relative to just writing out the fields. (We shouldn't be using alternatives to handle different fields!)
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -74,7 +74,6 @@ theorem reduction {m n : ℤ} (h1 : ProblemPredicate N m n) (h2 : 1 < n) :
obtain (rfl : m = n) | (h3 : m < n) := h1.m_le_n.eq_or_lt
· have h4 : m = 1 := h1.eq_imp_1
exact absurd h4.symm h2.ne
- -- Porting note: Original proof used `refine_struct { n_range := h1.m_range .. }`
exact
{ n_range := h1.m_range
m_range := by
Fix also some names in RingTheory.Polynomial.Eisenstein.Basic
that are in the wrong namespace.
@@ -11,6 +11,7 @@ Authors: Kevin Lacker
import Mathlib.Data.Int.Lemmas
import Mathlib.Data.Nat.Fib
import Mathlib.Tactic.Linarith
+import Mathlib.Tactic.LinearCombination
/-!
# IMO 1981 Q3
@@ -57,20 +58,14 @@ variable {N}
theorem m_le_n {m n : ℤ} (h1 : ProblemPredicate N m n) : m ≤ n := by
by_contra h2
- have h3 : 1 = (n * (n - m) - m ^ 2) ^ 2 := by
- calc
- 1 = (n ^ 2 - m * n - m ^ 2) ^ 2 := h1.eq_one.symm
- _ = (n * (n - m) - m ^ 2) ^ 2 := by ring
+ have h3 : 1 = (n * (n - m) - m ^ 2) ^ 2 := by linear_combination - h1.eq_one
have h4 : n * (n - m) - m ^ 2 < -1 := by nlinarith [h1.n_range.left]
have h5 : 1 < (n * (n - m) - m ^ 2) ^ 2 := by nlinarith
exact h5.ne h3
#align imo1981_q3.problem_predicate.m_le_n Imo1981Q3.ProblemPredicate.m_le_n
theorem eq_imp_1 {n : ℤ} (h1 : ProblemPredicate N n n) : n = 1 :=
- haveI : n * (n * (n * n)) = 1 := by
- calc
- _ = (n ^ 2 - n * n - n ^ 2) ^ 2 := by simp [sq, mul_assoc]
- _ = 1 := h1.eq_one
+ have : n * (n * (n * n)) = 1 := by linear_combination h1.eq_one
eq_one_of_mul_eq_one_right h1.m_range.left.le this
#align imo1981_q3.problem_predicate.eq_imp_1 Imo1981Q3.ProblemPredicate.eq_imp_1
@@ -89,10 +84,7 @@ theorem reduction {m n : ℤ} (h1 : ProblemPredicate N m n) (h2 : 1 < n) :
_ < n := sub_lt_self n h1.m_range.left
_ ≤ N := h1.n_range.right
exact ⟨h5, h6.le⟩
- eq_one := by
- calc
- _ = (n ^ 2 - m * n - m ^ 2) ^ 2 := by ring
- _ = 1 := h1.eq_one }
+ eq_one := by linear_combination h1.eq_one }
#align imo1981_q3.problem_predicate.reduction Imo1981Q3.ProblemPredicate.reduction
end ProblemPredicate
The unported dependencies are